Weak signed Roman k-domatic number of a graph

Document Type : Original paper

Author

RWTH Aachen University

Abstract

Let k≥1 be an integer. A { weak signed Roman k-dominating function} on a graph G is
a function  f:V(G)⟶{−1,1,2} such that ∑u∈N[v]f(u)≥k for every
v∈V(G), where N[v] is the closed neighborhood of v.
A set {f1,f2,…,fd} of distinct weak signed Roman k-dominating
functions on G with the property that ∑i=1dfi(v)≤k for each v∈V(G), is called a
{ weak signed Roman k-dominating family} (of functions) on G. The maximum number of functions
in a  weak signed Roman k-dominating family on G is the { weak signed Roman k-domatic number} of G,
denoted by dwsRk(G). In this paper we initiate the study of the weak signed Roman k-domatic number
in graphs, and we present sharp bounds for dwsRk(G). In addition, we determine the weak signed Roman
k-domatic number of some graphs.

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Main Subjects

References

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Communications in Combinatorics and Optimization
Volume 7, Issue 1
June 2022
Pages 17-27

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